一个格子KdV方程的拉克斯对（英文）  

The Lax Pair of a Lattice KdV Equation

作　　者：白永强[1,2] 刘元元 裴明 

机构地区：[1]河南大学现代数学研究所,河南开封475004 [2]河南大学数学与统计学院,河南开封475004

出　　处：《河南大学学报（自然科学版）》2015年第4期384-389,共6页Journal of Henan University:Natural Science

基　　金：supported by National Natural Science Foundation of China(10801045)

摘　　要：微分几何和微分形式在数学物理中起着十分重要的作用,它们可以作为工具用来讨论许多重要的微分方程,讨论方程的可积性、求微分方程的不变量和对称子等.非线性演化方程的可积性检验是可积系统理论中的一个重要课题,有着许多方法,其中延拓结构理论是迄今为止求非线性演化方程拉克斯对或者检验方程拉克斯可积性的一种重要方法.该理论主要利用连续微积分和微分形式,在非交换微分和非交换微分形式的基础上,给出了一种求离散非线性演化方程的线性特征值或者拉克斯对的类似方法.由此检验了该差分方程的拉克斯可积性.另外,还利用这一理论讨论了KdV方程的一个离散模型,并且求得了其拉克斯对.Differential geometry and differential forms are of great importance in mathematical physics, and they can be used to discuss many important differential equations, to test their integrability, to get their invariants and symmetry. The integrability test of differential equations is also an important topic and there exist many methods at now. The prolongation structure theory is an important method to obtain the Lax pair of nonlinear evolution equations up to now. The theory used mainly continuous differential calculus and differential forms. Based on noncommutative differential calculus and differential forms, we propose a similar method for obtaining the linear eigenvalue problem or the Lax pair associating with discrete nonlinear evolution equations. The Lax integrability of difference equations is thus tested. In this paper, we discuss a discrete model of the KdV equation by means of this methodology, and obtain the corresponding Lax pair.

关 键 词：非交换微分 可积性 拉克斯对 

分 类 号：O175.7[理学—数学]